TY - JOUR

T1 - Edge proximity and matching extension in punctured planar triangulations

AU - Aldred, R. E.L.

AU - Fujisawa, Jun

AU - Saito, Akira

N1 - Funding Information:
The second author's work was supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B) 16H03952 and Grant-in-Aid for Young Scientists (B) 26800085. The third author's work was supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C) 25330017.
Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2017/12

Y1 - 2017/12

N2 - A matching M in a graph G is said to be extendable if there exists a perfect matching of G containing M. In 1989, it was shown that every connected planar graph with at least 8 vertices has a matching of size three which is not extendable. In contrast, the study of extending certain matchings of size three or more has made progress in the past decade when the given graph is 5-connected planar triangulation or 5-connected plane graphs with few non-triangular faces. In this paper, we prove that if G is a 5-connected plane graph of even order in which at most two faces are not triangular and M is a matching of size four in which the edges lie pairwise distance at least three apart, then M is extendable. A related result concerning perfect matching with proscribed edges is shown as well.

AB - A matching M in a graph G is said to be extendable if there exists a perfect matching of G containing M. In 1989, it was shown that every connected planar graph with at least 8 vertices has a matching of size three which is not extendable. In contrast, the study of extending certain matchings of size three or more has made progress in the past decade when the given graph is 5-connected planar triangulation or 5-connected plane graphs with few non-triangular faces. In this paper, we prove that if G is a 5-connected plane graph of even order in which at most two faces are not triangular and M is a matching of size four in which the edges lie pairwise distance at least three apart, then M is extendable. A related result concerning perfect matching with proscribed edges is shown as well.

KW - Distance restricted matching extension

KW - Plane graph

KW - Punctured triangulation

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U2 - 10.1016/j.disc.2017.07.017

DO - 10.1016/j.disc.2017.07.017

M3 - Article

AN - SCOPUS:85027441616

VL - 340

SP - 2978

EP - 2985

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 12

ER -